Simplify ((24a^3b^8)/(6a^5b))((4b^3a)/(2a^3))

$(\frac{24 a^{3} \cdot b^{8}}{6 a^{5} \cdot b}) \cdot (\frac{4 b^{3} \cdot a}{2 a^{3}})$

Step 1

Combine.

$\frac{24 a^{3} \cdot b^{8} (4 b^{3} \cdot a)}{6 a^{5} \cdot b (2 a^{3})}$

Step 2

Multiply

$a^{3}$ by

$a$ by adding the exponents.

Move

$a$ .

$\frac{24 (a \cdot a^{3}) \cdot b^{8} (4 b^{3})}{6 a^{5} \cdot b (2 a^{3})}$

Multiply

$a$ by

$a^{3}$ .

Raise

$a$ to the power of

$1$ .

$\frac{24 (a^{1} a^{3}) \cdot b^{8} (4 b^{3})}{6 a^{5} \cdot b (2 a^{3})}$

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{24 a^{1 + 3} \cdot b^{8} (4 b^{3})}{6 a^{5} \cdot b (2 a^{3})}$

Add

$1$ and

$3$ .

$\frac{24 a^{4} \cdot b^{8} (4 b^{3})}{6 a^{5} \cdot b (2 a^{3})}$

Step 3

Multiply

$b^{8}$ by

$b^{3}$ by adding the exponents.

Move

$b^{3}$ .

$\frac{24 a^{4} \cdot (b^{3} b^{8}) \cdot 4}{6 a^{5} \cdot b (2 a^{3})}$

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{24 a^{4} \cdot b^{3 + 8} \cdot 4}{6 a^{5} \cdot b (2 a^{3})}$

Add

$3$ and

$8$ .

$\frac{24 a^{4} \cdot b^{11} \cdot 4}{6 a^{5} \cdot b (2 a^{3})}$

Step 4

Multiply

$a^{5}$ by

$a^{3}$ by adding the exponents.

Move

$a^{3}$ .

$\frac{24 a^{4} \cdot b^{11} \cdot 4}{6 (a^{3} a^{5}) \cdot b \cdot 2}$

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{24 a^{4} \cdot b^{11} \cdot 4}{6 a^{3 + 5} \cdot b \cdot 2}$

Add

$3$ and

$5$ .

$\frac{24 a^{4} \cdot b^{11} \cdot 4}{6 a^{8} \cdot b \cdot 2}$

Step 5

Cancel the common factor of

$24$ and

$6$ .

Factor

$6$ out of

$24 a^{4} \cdot b^{11} \cdot 4$ .

$\frac{6 (4 a^{4} \cdot b^{11} \cdot 4)}{6 a^{8} \cdot b \cdot 2}$

Cancel the common factors.

Factor

$6$ out of

$6 a^{8} \cdot b \cdot 2$ .

$\frac{6 (4 a^{4} \cdot b^{11} \cdot 4)}{6 (a^{8} \cdot b \cdot 2)}$

Cancel the common factor.

$\frac{6 (4 a^{4} \cdot b^{11} \cdot 4)}{6 (a^{8} \cdot b \cdot 2)}$

Rewrite the expression.

$\frac{4 a^{4} \cdot b^{11} \cdot 4}{a^{8} \cdot b \cdot 2}$

Step 6

Cancel the common factor of

$4$ and

$2$ .

Factor

$2$ out of

$4 a^{4} \cdot b^{11} \cdot 4$ .

$\frac{2 (2 a^{4} \cdot b^{11} \cdot 4)}{a^{8} \cdot b \cdot 2}$

Cancel the common factors.

Factor

$2$ out of

$a^{8} \cdot b \cdot 2$ .

$\frac{2 (2 a^{4} \cdot b^{11} \cdot 4)}{2 \cdot (a^{8} \cdot b)}$

Cancel the common factor.

$\frac{2 (2 a^{4} \cdot b^{11} \cdot 4)}{2 \cdot (a^{8} \cdot b)}$

Rewrite the expression.

$\frac{2 a^{4} \cdot b^{11} \cdot 4}{a^{8} \cdot b}$

Step 7

Cancel the common factor of

$a^{4}$ and

$a^{8}$ .

Factor

$a^{4}$ out of

$2 a^{4} \cdot b^{11} \cdot 4$ .

$\frac{a^{4} (2 \cdot b^{11} \cdot 4)}{a^{8} \cdot b}$

Cancel the common factors.

Factor

$a^{4}$ out of

$a^{8} \cdot b$ .

$\frac{a^{4} (2 \cdot b^{11} \cdot 4)}{a^{4} (a^{4} \cdot b)}$

Cancel the common factor.

$\frac{a^{4} (2 \cdot b^{11} \cdot 4)}{a^{4} (a^{4} \cdot b)}$

Rewrite the expression.

$\frac{2 \cdot b^{11} \cdot 4}{a^{4} \cdot b}$

Step 8

Cancel the common factor of

$b^{11}$ and

$b$ .

Factor

$b$ out of

$2 \cdot b^{11} \cdot 4$ .

$\frac{b (2 \cdot b^{10} \cdot 4)}{a^{4} \cdot b}$

Cancel the common factors.

Factor

$b$ out of

$a^{4} \cdot b$ .

$\frac{b (2 \cdot b^{10} \cdot 4)}{b \cdot a^{4}}$

Cancel the common factor.

$\frac{b (2 \cdot b^{10} \cdot 4)}{b \cdot a^{4}}$

Rewrite the expression.

$\frac{2 \cdot b^{10} \cdot 4}{a^{4}}$

Step 9

Multiply

$4$ by

$2$ .

$\frac{8 b^{10}}{a^{4}}$

Simplify ((24a^3*b^8)/(6a^5*b))*((4b^3*a)/(2a^3))

Related Questions

Simplify ((24a^3b^8)/(6a^5b))((4b^3a)/(2a^3))